This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse-Smale systems and complete and refinable abstractions for linear systems are shown.
|Title of host publication||2010 49th IEEE Conference on Decision and Control, CDC 2010|
|Number of pages||6|
|Publication status||Published - 2010|
|Event||2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States|
Duration: 15. Dec 2010 → 17. Dec 2010
|Conference||2010 49th IEEE Conference on Decision and Control, CDC 2010|
|Period||15/12/2010 → 17/12/2010|